Ususally the mantal(outside covering) is too slick to be good for griping with hands however striping the cover and and braiding the Core would be a good if not time consuming option but I think would still be very abusive to your hands.

Not too stretchy? Seems like the dynamic quality of a modern climbing (belay) rope is at odds with what you want for a gym-climbing rope. I guess 4 braided together would be 1/4 as responsive to loading.